A Symmetrohedron Featuring Regular Heptagons, Regular Hexagons, Irregular Hexagons, and Irregular Pentagon-Pairs

symmetrohedron featuring heptagons hexagons and pentagons

Symmetrohedra are symmetric polyhedra which have regular polygons for most (but not necessarily all) of their faces. I made this particular one using Stella 4d, which you can try for yourself at this website. Here’s the net for this polyhedron, also.

symmetrohedron featuring heptagons hexagons and pentagons net

This particular symmetrohedron features twelve faces which are regular heptagons, and eight faces which are regular hexagons (shown in yellow). The irregular faces are 24 pentagons, arranged in a dozen pairs, as well as the six green hexagons. That’s 50 faces in all. This solid has pyritohedral symmetry. The most unusual thing about this polyhedron are its 12 heptagonal faces.